Rock-scissors-paper game on regular small-world networks

G. Szabó, A. Szolnoki, Rudolf Izsák

Research output: Contribution to journalArticle

129 Citations (Scopus)

Abstract

The spatial rock-scissors-paper game (or cyclic Lotka-Volterra system) is extended to study how the spatiotemporal patterns are affected by the rewired host lattice providing uniform number of neighbours (degree) at each site. On the square lattice this system exhibits a self-organizing pattern with equal concentration of the competing strategies (species). If the quenched background is constructed by substituting random links for the nearest-neighbour bonds of a square lattice then a limit cycle occurs when the portion of random links exceeds a threshold value. This transition can also be observed if the standard link is replaced temporarily by a random one with a probability P at each step of iteration. Above a second threshold value of P the amplitude of global oscillation increases with time and finally the system reaches one of the homogeneous (absorbing) states. In this case the results of Monte Carlo simulations are compared with the predictions of the dynamical cluster technique evaluating all the configuration probabilities on one-, two-, four- and six-site clusters.

Original languageEnglish
Pages (from-to)2599-2609
Number of pages11
JournalJournal of Physics A: Mathematical and General
Volume37
Issue number7
DOIs
Publication statusPublished - Feb 20 2004

Fingerprint

Small-world networks
Small-world Network
games
Rocks
rocks
Game
Threshold Value
Square Lattice
Spatio-temporal Patterns
thresholds
Lotka-Volterra System
organizing
Self-organizing
Absorbing
Limit Cycle
iteration
Nearest Neighbor
Exceed
Monte Carlo Simulation
Oscillation

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Rock-scissors-paper game on regular small-world networks. / Szabó, G.; Szolnoki, A.; Izsák, Rudolf.

In: Journal of Physics A: Mathematical and General, Vol. 37, No. 7, 20.02.2004, p. 2599-2609.

Research output: Contribution to journalArticle

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